Molecular packing coefficient

Figure 19. Rotational viscosity coefficient y at 25 °C as a function of the free volume coefficient Vfg = 1 - fcp, where is the molecular packing coefficient (1) al-kyloxycyanobiphenyls (2) alkylbicyclooctylcyano-benzenes (3) alkylpyridylcyanobenzenes (4) alkylcyanobiphenyls (5) alkylcyclohexylcyanobenzenes. The crosses show the rotational viscosity for some members of the homologous series and the lengths of the vertical lines give the accuracy of measurement.

Figure 1.3. Dependence of molecular packing coefficient Kp at 20°C on the Van-der-Vaals molecular volume Vv for homologous rows of organic compounds with linear aliphatic chains and various nature of end groups 1- amides 2- acids 3 - anhydrides 4 - alcohols 5 - nitriles 6 - iodides 7 - esters 8 -aldehydes 8 - bromides 9 - ketones 11 - amines 12 - chlorides 13 - phtorides 14 - alkyl oxides.

Micellization is a second-order or continuous type phase transition. Therefore, one observes continuous changes over the course of micelle fonnation. Many experimental teclmiques are particularly well suited for examining properties of micelles and micellar solutions. Important micellar properties include micelle size and aggregation number, self-diffusion coefficient, molecular packing of surfactant in the micelle, extent of surfactant ionization and counterion binding affinity, micelle collision rates, and many others. 

As mentioned above, the powder SHG method is a useful technique for the screening of second-order nonlinear materials. However, because of the sensitivity of the SHG coefficients of crystalline materials to the orientational aspects of the molecular packing and because the measurement is performed on an essentially random distribution of microcrystalline particles, the powder SHG method is not generally useful for obtaining information about molecular hyperpolarizabilities. 

As molecular packing calculations involve just simple lattice energy minimizations another set of tests have focused on the finite temperature effects. For this purpose, Sorescu et al. [112] have performed isothermal-isobaric Monte Carlo and molecular dynamics simulations in the temperature range 4.2-325 K, at ambient pressure. It was found that the calculated crystal structures at 300 K were in outstanding agreement with experiment within 2% for lattice dimensions and almost no rotational and translational disorder of the molecules in the unit cell. Moreover, the space group symmetry was maintained throughout the simulations. Finally, the calculated expansion coefficients were determined to be in reasonable accord with experiment. 

This remarkable finding is accounted for by the open nature of the crystal structures, resulting from the steric effect of substituents, as attested by packing coefficients and molecular modelling. 

In protein crystals, due to the large size of the molecule, the empty space can have cross sections of 10-15 A or greater. The empty space between the protein molecules is occupied by mother liquor. This property of protein crystals, shared by nucleic acids and viruses, is otherwise unique among the crystal structures. In fact, the values of the packing coefficient of protein crystals range from 0.7 to 0.2, but the solvent molecules occupy the empty space so that the total packing coefficient is close to 1 [37]. Nevertheless, a detailed theoretical study has been carried out to examine the models of DNA-DNA molecular interactions on the basis of hard-sphere contact criteria. The hard-sphere computations are insufficient for qualitative interpretation of the packing of DNA helices in the solid state, but... 

The so-called coefficient of molecular packing (k) has proved useful in characterizing molecular packing. It is expressed in the following... 

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